2017-09-27T01:23:55Zhttp://cmde.tabrizu.ac.ir/?_action=export&rf=summon&issue=6632015-04-01Computational Methods for Differential EquationsComput. Methods Differ. Equ.2345-39822345-3982201532Some new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equationMinaMortazaviMohammadMirzazadeh‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by jacobi elliptic functions for the 1D MCGL equation are derived. Homogeneous method is a powerful method, it can be used to construct a large families of exact solutions to different nonlinear differential equations that does not involve independent variables.Exact traveling wave Solutions‎‎Modified Complex Ginzburg-Landau equation‎‎$(G'/G)$‎-‎expanson methodHomogeneous balance methodEextended F-expansion method201504017086http://cmde.tabrizu.ac.ir/article_4017_0464648f9f5a70082b84fd3112ca2dcf.pdf2015-04-01Computational Methods for Differential EquationsComput. Methods Differ. Equ.2345-39822345-3982201532Optimization with the time-dependent Navier-Stokes equations as constraintsMitraVizhehSyaed HodjatollahMomeni-MasulehAlaeddinMalekIn this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the optimal control of the Navier-Stokes equations is proposed. Numerical examples are given to demonstrate the efficiency of the method.Optimal Control ProblemsNavier-Stokes equationsPDE-constrained optimizationquasi-Newton algorithmfinite difference201504018798http://cmde.tabrizu.ac.ir/article_4484_0de495e641081aae07a2b511ceceb9bf.pdf2015-04-01Computational Methods for Differential EquationsComput. Methods Differ. Equ.2345-39822345-3982201532Application of the block backward differential formula for numerical solution of Volterra integro-differential equationsSomayyehFazeliIn this paper, we consider an implicit block backward differentiation formula (BBDF) for solving Volterra Integro-Differential Equations (VIDEs). The approach given in this paper leads to numerical methods for solving VIDEs which avoid the need for special starting procedures. Convergence order and linear stability properties of the methods are analyzed. Also, methods with extensive stability region of orders 2, 3 and 4 are constructed which are suitable for solving stiff VIDEs.Volterra integro-differential equationsBlock methodsBackward differential formula2015040199100http://cmde.tabrizu.ac.ir/article_4541_07598b31f5bf268f9053f664f3870864.pdf2015-04-01Computational Methods for Differential EquationsComput. Methods Differ. Equ.2345-39822345-3982201532Numerical solution of time-dependent foam drainage equation (FDE)MuratGubesYildirayKeskinGalipOturancReduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear partial differential equations (PDEs), it can be applied very easily and it has less computational work than other existing methods like Adomian decomposition and Laplace decomposition. Additionally, effectiveness and precision of RDTM solutions are shown in tables and graphically.Foam Drainage EquationLaplace Decomposition MethodAdomian Decomposition MethodReduced Differential Transform Method20150401111122http://cmde.tabrizu.ac.ir/article_4648_efda79e599c82bb21304dce4c2502549.pdf2015-04-01Computational Methods for Differential EquationsComput. Methods Differ. Equ.2345-39822345-3982201532Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problemRahmatDarziBahramAgheliIn this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0Boundary value problemfixed point theoremPartially ordered setPositive solutionnondecreasing solution20150401123133http://cmde.tabrizu.ac.ir/article_4649_30ab2f42a41eb1f68dba3f0aab9d34fc.pdf2015-04-01Computational Methods for Differential EquationsComput. Methods Differ. Equ.2345-39822345-3982201532Multi soliton solutions, bilinear Backlund transformation and Lax pair of nonlinear evolution equation in (2+1)-dimensionManjitSinghAs an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of associated linear problem or Lax pair are presented in straightforward manner and finally for proposed nonlinear equation, explicit one, two and three soliton solutions are also obtained.Soliton solutionsBilinear Backlund transformationsLax pairsPerturbation expansion20150401134146http://cmde.tabrizu.ac.ir/article_4769_c037a3bd2246ff1cd130bac4856a2745.pdf